Atkinson resistance is a practical resistance coefficient used in mine ventilation to describe how much pressure is lost when air flows through an airway. Instead of working directly with friction factors and detailed fluid mechanics each time, engineers group all the effects of length, size, roughness and fittings into a single value called Atkinson resistance, usually written as R. This coefficient is used in the relationship between pressure drop and airflow that is widely known as Atkinson's equation.
In its most common form, Atkinson's equation is written as:
Δp = R × Q²
where Δp is the pressure drop along an airway, Q is the airflow through that airway and R is the Atkinson resistance. The equation shows that pressure losses increase with the square of airflow, which matches the behaviour of turbulent flow typically found in mine drifts, raises, shafts and ventilation ducts. A higher R means the airway offers more resistance to flow, so more fan pressure is needed to move the same quantity of air.
Atkinson resistance depends on several physical factors. Long, narrow airways with rough rock walls will have a high resistance, while short, large cross section airways with smooth concrete lining will have a much lower resistance. Bends, doors, regulators, equipment and duct transitions also add to resistance. In practice R is often expressed in units that combine pressure, flow and length so that it can be used directly in ventilation network calculations without repeated unit conversions.
To use Atkinson resistance in design, engineers either estimate R from geometry and roughness using established formulas, or determine it empirically from ventilation surveys. If airflow and pressure drop are measured for an airway, the corresponding R can be calculated by rearranging the equation. Once R values are known for all branches in the mine ventilation network, they can be combined with fan characteristics to predict how air will distribute through the system.
Atkinson resistance is especially important in network analysis and fan selection. By summing RQ² terms around loops and enforcing continuity at junctions, engineers can identify which routes are bottlenecks, how much pressure main fans must generate, and whether auxiliary or booster fans are needed. Changing the size or lining of an airway directly changes its Atkinson resistance, so R is also a convenient way to assess the benefit of capital projects such as enlarging drifts or installing smooth concrete lining.
In summary, Atkinson resistance is the key resistance coefficient in mine ventilation calculations. It captures the combined effect of airway length, size, roughness and fittings into a single value used in the equation Δp = R × Q², making design and analysis of mine ventilation systems more straightforward.
